export interface Monoidal<F> extends Functor<F> {
  readonly unit: () => HKT<F, void>
  readonly mult: <A, B>(fa: HKT<F, A>, fb: HKT<F, B>) => HKT<F, [A, B]>
}

export interface Monoidal1<F extends URIS> extends Functor1<F> {
  readonly unit: () => Type<F, void>
  readonly mult: <A, B>(fa: Type<F, A>, fb: Type<F, B>) => Type<F, [A, B]>
}

export interface Monoidal2<F extends URIS2> extends Functor2<F> {
  readonly unit: <L>() => Type2<F, L, void>
  readonly mult: <L, A, B>(fa: Type2<F, L, A>, fb: Type2<F, L, B>) => Type2<F, L, [A, B]>
}

export interface Monoidal2C<F extends URIS2, L> extends Functor2C<F, L> {
  readonly unit: () => Type2<F, L, void>
  readonly mult: <A, B>(fa: Type2<F, L, A>, fb: Type2<F, L, B>) => Type2<F, L, [A, B]>
}

export interface Monoidal3<F extends URIS3> extends Functor3<F> {
  readonly unit: <U, L>() => Type3<F, U, L, void>
  readonly mult: <U, L, A, B>(fa: Type3<F, U, L, A>, fb: Type3<F, U, L, B>) => Type3<F, U, L, [A, B]>
}

export interface Monoidal3C<F extends URIS3, U, L> extends Functor3C<F, U, L> {
  readonly unit: () => Type3<F, U, L, void>
  readonly mult: <A, B>(fa: Type3<F, U, L, A>, fb: Type3<F, U, L, B>) => Type3<F, U, L, [A, B]>
}

export function fromApplicative<F extends URIS3>(applicative: Applicative3<F>): Monoidal3<F>
export function fromApplicative<F extends URIS2>(applicative: Applicative2<F>): Monoidal2<F>
export function fromApplicative<F extends URIS>(applicative: Applicative1<F>): Monoidal1<F>
export function fromApplicative<F>(applicative: Applicative<F>): Monoidal<F> { ... }

export function toApplicative<F extends URIS3>(monoidal: Monoidal3<F>): Applicative3<F>
export function toApplicative<F extends URIS2>(monoidal: Monoidal2<F>): Applicative2<F>
export function toApplicative<F extends URIS>(monoidal: Monoidal1<F>): Applicative1<F>
export function toApplicative<F>(monoidal: Monoidal<F>): Applicative<F> { ... }